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<h3 class="heading"><span class="type">Paragraph</span></h3>
<p>Let <span class="process-math">\(\alpha=1\text{.}\)</span> If <span class="process-math">\(f(x)= x\)</span> on <span class="process-math">\([0,L]\text{,}\)</span> then the solution is</p>
<div class="displaymath process-math" data-contains-math-knowls="">
\begin{equation*}
u(x,t)=\sum_{n=1}^{\infty}C_n e^{-\frac{n^2\pi^2t}{L^2}}\sin\dfrac{n\pi x}{L},\qquad n=1,2,3,\cdots
\end{equation*}
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<p class="continuation">where</p>
<div class="displaymath process-math" data-contains-math-knowls="">
\begin{equation*}
C_n=\frac{2L}{n\pi}(-1)^{n+1}.
\end{equation*}
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<p class="continuation">based on the result of the Fourier sine expansion in the last example from Section <code class="code-inline tex2jax_ignore">[cross-reference to target(s) "hrex1" missing or not unique]</code>.</p>
<span class="incontext"><a href="sec7_7.html#p-415" class="internal">in-context</a></span>
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